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Discontinuous Nash equilibrium points for nonzero-sum stochastic differential games

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  • Hamadène, Said
  • Mu, Rui

Abstract

In this paper, we study a nonzero-sum stochastic differential game in the Markovian framework. We show the existence of a discontinuous Nash equilibrium point for this game. The main tool is the notion of backward stochastic differential equations which, in our case, are multidimensional with discontinuous generators with respect to z component.

Suggested Citation

  • Hamadène, Said & Mu, Rui, 2020. "Discontinuous Nash equilibrium points for nonzero-sum stochastic differential games," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6901-6926.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:11:p:6901-6926
    DOI: 10.1016/j.spa.2020.07.003
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    References listed on IDEAS

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    5. Pierre Cardaliaguet & Slawomir Plaskacz, 2003. "Existence and uniqueness of a Nash equilibrium feedback for a simple nonzero-sum differential game," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 33-71, December.
    6. Jia, Guangyan, 2008. "A class of backward stochastic differential equations with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 231-237, February.
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    9. Paola Mannucci, 2014. "Nash Points for Nonzero-Sum Stochastic Differential Games with Separate Hamiltonians," Dynamic Games and Applications, Springer, vol. 4(3), pages 329-344, September.
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    Cited by:

    1. Hu, Zuopeng & Yang, Yanlong, 2024. "Existence and generic stability of open-loop Nash equilibria for noncooperative fuzzy differential games," Applied Mathematics and Computation, Elsevier, vol. 463(C).

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